# What is the Schauder estimate on usual Hölder space for parabolic type equations

What is the Schauder estimate on usual Holder space for parabolic type equations ?

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There are books on this. Read them, and come back if you have a more specific question. –  Michael Renardy Jun 14 '12 at 10:04
Dear Michael, I have seen some theorems for parabolic type but not for usual Hölder space, for instance we have Schauder estimate for $C^{k,l,\alpha}$ but In my question I am looking such theorem on usual Holder space – –  Hassan Jolany Jun 14 '12 at 10:10
Why do you need them on the usual Holder spaces? There is a reason why the preferred parabolic scaling is chosen and used. Perhaps if you motivate the question a bit more people would be more interested. –  Willie Wong Jun 14 '12 at 11:55
What you need as a first step is to try to find inclusions between the parabolic and the "usual" Hölder spaces. –  timur Jun 19 '12 at 0:10
That paper of Cao is not really well-written on this point, so you should not try to understand it literally. The correct way to do it is like in the paper of Chau. What bothers you about parabolic Holder spaces? They are the natural ones to use for parabolic equations. There are some easy and elementary inclusions with the "usual" spaces, as timur says. –  YangMills Jul 6 '12 at 17:34